19 of the Russian's 21 titles have been won on hardcourt
A revitalized Medvedev claimed his maiden title for over two years with victory over Frenchman Moutet in the Almaty Open title decider.
The Russian, a ex- top-ranked player, has experienced a difficult season, achieving just a single victory at the big events and experiencing a difficult moment at the US Open.
Medvedev's inconsistency on the ATP Tour - and struggles with his serve in particular - caused him falling of the world's top 10 and eventually parting ways with long-time mentor his previous coach.
Now training with Thomas Johansson and his other coach, the tennis star has consistently progressed in the past month - climaxing in a tightly fought 7-5 4-6 6-3 win over opponent Moutet.
This represents Medvedev's maiden championship following the Italian tournament and initial on a hardcourt since spring of that year.
The win also signifies Medvedev has achieved 21 titles at twenty-one distinct tournaments.
"This marks the first occasion I have attended a tournament with my two daughters at once, so to win a trophy is particularly special," commented tennis professional Medvedev.
"This victory is in dedication of my second daughter Victoria, because the initial championship I got when my older daughter Alisa was delivered was for her."
The athlete, the 2021 US Open champion, had lost his past six title deciders, featuring in the German tournament previously this season.
Medvedev's retrieving strategy and frequent emotional displays on the tennis court had led some to wonder if his skill to perform at the highest level was finished.
Yet the athlete has implemented adjustments in recent weeks, striving to approach the net and perform positively, backed up by an enhanced serve.
He fought back from a deficit in the first set against the tricky Frenchman, securing 4 of the final five points to take the lead.
The competitors exchanged service breaks in the following set before the Frenchman, attempting for his first tour title, gained dominance to force a final set.
Moutet rescued four early-game chances in a competitive deciding set before the champion won the break to that score to secure the win.
Appropriately, the winner earned victory with a shot at the net, with his opponent incapable to manage a return after two hours and 38 minutes.